Eli5 why the coastline paradox is a paradox?
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My interpretation is that focusing on the math only is the wrong way to look at it.
For example, a well defined and very curvy shape will have an increased edge area as one uses smaller and smaller straight units of measure. However, because it’s well defined, this value will converge on a true value.
In the case of a real beach though, as you zoom in there are more and more boundaries to measure and the actual definition of what is coast and what is ocean becomes much less distinct. What grain of sand is the edge?
It’s possible that if we froze time and inspected the beach molecule by molecule, this particular paradox might no longer be defined as one. At least I believe at that scale eventually the measurement would converge to a true value.
I don’t believe this should count at all as a paradox though. It seems to be a description of a easily observable fact that boundaries are relative. Scale is a huge factor in any kind of measurement. However, I understand that Webster isn’t backing me up on my definition of paradox and that many such exceptions apply.
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